Design and computation of near-optimal stable observers for bilinear systems

In the paper, the problem of designing full-order observers for multivariable bilinear control systems is transformed into a nonlinear constrained optimisation problem. It is shown that an appropriate choice of the objective function, based on an exponentially decaying bound on the norm of the observer error, together with the selection of a suitable set of constraints, ensures that the solution of the transformed problem not only satisfies the usually desired design criterion of global asymptotic stability of the observer error dynamics, but it can also yield observers with near-optimum rate of decay of the error norm. These findings are confirmed in results presented from a graphically supported numerical computer package for automatic design and display of the near-optimal stable observer trajectories in the bivariate case.